Chapter 8 - Decomposition of Measures Flashcards
State Lemma 8.2 - The Parallelogram Law.
Define a closed subset of normed L^2.
State Proposition 8.3 on orthogonal subspaces.
Define a Bounded Linear Map.
What is the relationship between boundedness and continuity?
State Theorem 8.4 - Reisz Representation Theorem.
State Lemma 8.5 - How do you integrate wrt a finite sum of measures?
State Lemma 8.6 - How do you integrate wrt the restriction of a measure?
State Theorem 8.7 - The RNL Theorem for finite measures.
State Theorem 8.8 - The RNL Theorem for sigma-finite measures.
Define Absolute Continuity.
Define mu and v being singular wrt eachother.
State Theorem 8.9 - The RN Theorem for sigma-finite measures.
Define the Radon-Nikodym derivative of v wrt mu.
State Theorem 8.10 - Lebesgue’s Decomposition Theorem.
